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Byju's Answer
Standard XII
Mathematics
Area between Two Curves
Find the volu...
Question
Find the volume of the parallelopiped whose coterminals edges are represented by the vectors
→
a
=
^
i
−
2
^
j
+
^
3
→
b
=
−
2
^
i
+
3
^
j
−
4
^
k
→
c
=
^
i
−
3
^
j
+
5
^
k
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Solution
Consider the problem
as we know that area of parallelopiped whose three sides are
→
a
,
→
b
and
→
c
equal to
∣
∣
[
→
a
→
b
→
c
]
∣
∣
And as we have
→
a
=
^
i
−
2
^
j
+
3
^
k
→
b
=
−
2
^
i
+
3
^
j
−
4
^
k
→
c
=
^
i
−
3
^
j
+
5
^
k
Now,
∣
∣
[
→
a
→
b
→
c
]
∣
∣
=
∣
∣ ∣
∣
1
−
2
3
−
2
3
−
4
1
−
3
5
∣
∣ ∣
∣
=
1
(
15
−
12
)
+
2
(
−
10
+
4
)
+
3
(
6
−
3
)
=
3
−
12
+
9
=
0
Hence volume
=
0
sq. units
Suggest Corrections
0
Similar questions
Q.
Find the volume of a parallelopiped whose edges are represented by the vectors :
→
a
=
2
^
i
−
3
^
j
−
4
^
k
,
→
b
=
^
i
+
2
^
j
−
^
k
,
and
→
c
=
3
^
i
+
^
j
+
2
^
k
.
Q.
The volume of the parallellopiped whose coterminal edges are
2
^
i
−
3
^
j
+
4
^
k
,
^
i
+
2
^
j
−
2
^
k
,
3
^
i
−
^
j
+
^
k
is
Q.
Find the volume of the parallelepiped whose coterminous edges are represented by vectors
→
a
=
^
i
+
^
j
+
^
k
;
→
b
=
2
^
i
+
4
^
j
−
^
k
and
→
c
=
^
i
+
^
j
+
3
^
k
Q.
The three vectors
→
A
=
3
^
i
−
2
^
j
+
^
k
,
→
B
=
^
i
−
3
^
j
+
5
^
k
and
→
C
=
2
^
i
−
^
j
+
4
^
k
form
Q.
Find the volume of the parallelopiped whose coterminus edges are given by vectors
2
^
i
+
3
^
j
−
4
^
k
,
5
^
j
+
7
^
j
+
5
^
k
and
4
^
i
+
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^
j
−
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^
k
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